Stability and scaling limits for Markov processes and applications (1–3 cr)

Lecturer:
Prof Matthieu Jonckheere (U Buenos Aires)

Schedule:
Three lectures during 24–26 Sep 2018, every day 10:15–12:00 (Mon, Tue, Wed)

Location:
Krossi lounge (M220), 2nd floor, Otakaari 1, Aalto University

Description:
Markov processes allow to study models of almost any dynamics: population dynamics, data networks, physical systems evolutions, biological networks, etc. We will study techniques to answer stability questions including techniques allowing to link some Markov processes to simpler systems (often a deterministic dynamical system) via space-time scaling.

Topics:
1) Markov processes in discrete and continuous time
2) Stationary measures, reversibility
3) Martingales for Markov processes
4) Lyapunov functions
5) Scaling limits
6) Stochastic stability

Evaluation: You may get 1 cr for active participation at the lectures, and up to 3 cr by doing a project (to be agreed with the lecturer).

Registration: You can send an email to lasse.leskela@aalto.fi or just show up at the first lecture.